[logic-ml] Kobe Colloquium on Logic, Statistics and Informatics, May 1 (Rod Downey)

[Joerg Brendle]

Kobe Colloquium on Logic, Statistics and Informatics

以下の要領でコロキウムを開催します。

日時：2013年5月1日（水）15:00-16:30
場所：神戸大学自然科学総合研究棟3号館4階421室（プレゼンテーション室）
講演者：Rod Downey (Victoria University of Wellington, New Zealand)

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題目：Effectively in Abelian Group Theory

アブストラクト：The effectiveness of the theory of abelian groups has been long
studied beginning with the work of Mal'cev in the 60's. Nevertheless many
problems
remain. In this lecture I will discuss ongoing work on questions of
effectiveness of
categoricity and presentability for computable torsion-free abelian groups
and for p-groups.
For example, for categoricity, general problem is impossible; for example
Downey and
Montalban showed that the isomorphism problem for torsion-free abelian
groups is
Sigma_1^1-complete. The principle difficulty lies in the lack of
invariants. However,
where there are  some invariants there we can salvage some effectiveness. The
groups
we look at are the completely decomposable ones, which have decompositions
of the
form oplus_{i in omega} G_i with G_i a subgroup of the additive group of
the rationals.
Such groups are called homogeneous if G_i=H for all i. Alexander Melnikov
and the
author have shown that homogeneous computable completely decomposable
groups are
always Delta_3^0 categorical, this bound is sharp, and have classified
when the groups
are Delta_2^0 categorical in terms of what are called semilow sets. In more
recent work,
we have shown that every computable completely decomposable group is
Delta_5^0
categorical and that this bound is sharp. Additionally we can show that
the index set
of such groups is Sigma_7^0. I will also describe ongoing work on Ulm's
Theorem.


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交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」
行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ．
http://www.kobe-u.ac.jp/info/access/rokko/rokkodai-dai2.htm

連絡先：ブレンドレ ヨーグ  brendle at kurt.scitec.kobe-u.ac.jp
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